Matrix transformations on some sequence spaces related to strong Cesàro summability and boundedness
type: Item
instance of: scholarly article
title: Matrix transformations on some sequence spaces related to strong Cesàro summability and boundedness
zbMATH Open document ID: 1171.40002
author: Eberhard Malkowsky
author: Bilal Altay
author: Feyzi Başar
published in: Applied Mathematics and Computation
publication date: 2009-06-09T00:00:00Z
review text: Recently \textit{C. Adydin} and \textit{F. Başar} [Appl. Math. Comput. 157, No.~3, 677--693 (2004; Zbl 1072.46007)] studied the matrix domain of a triangular matrix in the sets of sequences that are (i) summable to zero, (ii) summable and (iii) bounded by the Cesàro method of order one. \textit{I. J. Maddox} [J. Lond. Math. Soc. 43, 285-290 (1968; Zbl 0155.38802)] introduced and studied the above-mentioned class of sequences by the strong Cesàro method of order 1 with index \(p\), \(p\geq 1\). Here the authors discuss the class of sequences studied by C. Adydin and F. Basar for the strong Cesàro method of order 1 with index \(p\), \(p\geq 1\). They also determine the \(\beta\)-duals of the spaces studied and characterize matrix transformations on them into the sets of bounded, convergent and null sequences.
reviewed by: Ganesh Datta Dikshit
Mathematics Subject Classification ID: 40C05
Mathematics Subject Classification ID: 40H05
zbMATH DE Number: 5562972
zbMATH Keywords: matrix domain in a sequence space
zbMATH Keywords: \(\beta\)-duals
zbMATH Keywords: triangular matrix transformations
zbMATH Keywords: strong Cesàro summability with index
MaRDI profile type: Publication
full work available at URL: j.amc.2009.01.062
OpenAlex ID: W1972799610
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DOI: 10.1016/J.AMC.2009.01.062
description: scientific article; zbMATH DE number 5562972